Eg 3: A witness to a hit-and-run accident told the police that the license number contained 3 different
letters followed by 3 digits. What is the total number of plates that the police may have to check if
(a) the plate starts with and end with 13 ? [Ans: 6000 ]
(b) the digits are " ? [Ans: 15600 ]
© all the digits are odd numbers? [Ans: 1950000 ]
(d) the plate contained the letters RLH, the first digit was and the witness cannot recall the last 2
digits? [Ans: 600 ]

Known Conditions

• The license plate consists of 3 different letters followed by 3 digits.
• Letters can be any from the English alphabet (26 letters).
• Digits can be any from 0 to 9 (10 digits).

(a) The plate starts with and ends with 13

1. The first letter is fixed as .
2. The second letter can be any of the remaining 25 letters (since it must be different from ).
3. The third letter can be any of the remaining 24 letters (since it must be different from both and the second letter).
4. The last two digits are fixed as 13.

(b) The digits are “007”

1. The first letter can be any of the 26 letters.
2. The second letter can be any of the remaining 25 letters.
3. The third letter can be any of the remaining 24 letters.
4. The digits are fixed as “007”.

© All the digits are odd numbers

1. The first letter can be any of the 26 letters.
2. The second letter can be any of the remaining 25 letters.
3. The third letter can be any of the remaining 24 letters.
4. The digits must be odd. The odd digits are 1, 3, 5, 7, 9 (5 options).
5. Each of the 3 digits can be any of the 5 odd digits.

(d) The plate contained the letters RLH, the first digit was and the witness cannot recall the last 2 digits

1. The letters are fixed as RLH.
2. The first digit is fixed as .
3. The last two digits can be any digits from 0 to 9 (10 options each).

Summary of Results

• (a) Total plates: 600
• (b) Total plates: 15600
• © Total plates: 1950000
• (d) Total plates: 100

• (a) 600
• (b) 15600
• © 1950000
• (d) 100